For openers, you say that you have some birdshot cartridges loaded with 34 grams of 0/0. I am not sure what you have, but it sounds like you have some 00 (double ought) buckshot.
The 34 grams is probably the weight of the powder. Different powders can have more or less energy per gram, which is why equvalent loads may have more or less powder depending.
I rarely use buck and am not sure, but 34 grams seems to be a tad on the heavy side. What is your 12 gauge chambered to use; 2-3/4 or 3" shot shells? Be careful. 3 may fit a 2-3/4 chamber, but not when the petals of the shell unfold. Firing a 3 in a gun designed for 2-3/4 can result in dangerously high barrel pressures.
Shot shell boxes should be marked with equivalents, which tells you the powder's equivalence to an old black powder load.
I don't believe that total projectile weights have changed that much, but depending on the use you may need more boom boom to accomplish the same mission. Often regulations require steel shot and I undrstand, but may be totally wrong, that becasuse steel shot is less dense more muzzle energy is needed for some purposes, like hitting high flying fowl.
This may help. http://en.wikipedia.org/wiki/Shotgun_shell
You may want to post the make and model of your gun and specify that shotshell.